Question
An observer, $1.5m$ tall, is $28.5m$ away from a $30m$ high tower. Determine the angle of elevation of the top of the tower from the eye of the observer.
✓
Answer
Let $AB = 1.5m$ be the observer and $CD = 30m$ be the tower.
Let the angle of elevation of the top of the tower be $\alpha.$
$CD = CE + ED$
$\Rightarrow CD = CE + AB$
$\Rightarrow 30 = CE + 1.5$
$\Rightarrow CE = 30 - 1.5 = 28.5m$
In $\triangle\text{CEB,}$
$\tan\alpha=\frac{\text{CE}}{\text{BE}}=\frac{28.5}{28.5}$
$\Rightarrow\ \tan\alpha=1$
$\Rightarrow\ \tan\alpha=\tan45^\circ$
$\Rightarrow\ \alpha=45^\circ$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The shape of the cross section of a canal is a trapezium. If the canal is $10 \ m$ wide at the top, $6\ m$ wide at the bottom and the area of its cross section is $640m^2$, find the depth of the canal.
→In figure, find $tan\ P - cot\ R$.
→Very-Short and Short-Answer Qustions:
Write the value of $\sin^2\theta\cos^2\theta\big(1+\tan^2\theta\big)\big(1+\cot^2\theta\big)$
→Write the value of $\sin^2\theta\cos^2\theta\big(1+\tan^2\theta\big)\big(1+\cot^2\theta\big)$
Define $HCF$ of two positive integers and find the $HCF$ of the following pairs of numbers:
$105$ and $120$
→$105$ and $120$
Find the area of a rhombus whose diagonals are 48cm and 20cm long.
Very-short and Short-Answer Questions.
Write the value of $\text{cosec}^2\theta(1+\cos\theta)(1-\sin\theta).$
What is the smallest number that, when divided by $35, 56$ and $91$ leaves remainders of $7$ in each case?
→Find the roots of the following equations, if they exist, by applying the quadratic formula:
$x^2-4 x-1=0$
→$x^2-4 x-1=0$
Write the condition to be satisfied by $q$ so that a rational number $\frac{\text{p}}{\text{q}}$ has a terminating decimal expansion.
→Solve: $23x + 29y = 98, 29x + 23y =110$
→